1 chapter four understand the use and the importance of graphical presentation; recognise the...
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Chapter Four
understand the use and the importance of graphical presentation;
recognise the features of varies graphical presentations; and
organise and present the collected data in the most effectively way.
Graphical Presentation
GoalWhen you completed this chapter, you will be able to:
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Graphical Presentation
Problem Area
Collecting the data
Deriving the statistics
Communicating the results
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Graphics can be used as an effective method of visual communication
Graphical Presentation
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Summary Table
e.g.1 The numbers of reference books in the BA Departmental Library: 40 Statisticbooks, 25 Management books, 80 Accountancy books, 60 Insurance books, and45 other reference books.
Table: Frequency and percentage summary table for BA Departmental Library
Type of books No. of books Percentage of booksStatistic 40 16Management 25 10Accountancy 80 32Insurance 60 24Other 45 18Total 250 100
Note: there are table Title, Description for the table, and Column Heading listed.
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Scatter Diagram
The pattern of the scatter of the points provides insights into the existence and nature of the relationship between the two variables.
Scatter Diagram
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20
40
60
80
100
120
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hours of Study
Exam
. Sco
re
the independent variable X and dependent variable Y
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(a) Direct Linear
0
50
100
0 5 10 15 20
X
Y
(b) Inverse Linear
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50
100
0 5 10 15 20
X
Y
Scatter Diagram(2)
Possible relationships between two variables:
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(c) Direct Curvilinear
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50
100
150
200
0 5 10 15 20 25
X
Y
(d) Inverse Curvilinear
0
50
100
150
200
0 5 10 15 20 25
X
Y
Scatter Diagram (3)
Possible relationships between two variables:
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(e) Direct Linear with more scattering
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20
40
60
80
0 5 10 15 20 25
X
Y
(f) No Relationship
0
10
20
30
40
0 5 10 15 20 25
X
Y
Scatter Diagram (4)
Possible relationships between two variables:
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Line Chart
Line chart use lines between data points to depict the magnitudes of data for two variables or for one variable over time.
The height of the line allows the user to compare magnitude easily.
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(a) Line Chart depicting relationship between two variables
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5
10
15
20
25
30
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0 5 10 15 20 25 30 35 40 45
Income (in '000)
Sa
vin
g (
in '0
00
)
(b) Line Chart depicting Sales over Time
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10
20
30
40
50
1990 1991 1992 1993 1994
YearS
ale
s (
in m
illio
ns
)
It reflects the moving total, moving average with the seasonal variations taken out - it is the trend line.
Line Chart (2)
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Bar Chart
Bar chart is used to depict the magnitude of data for different qualitative categories or over time.
Several points to note :
1. Bar chart consists of vertical or horizontal bars.
2. all bars should be in same width, but the width of each bar has no special meaning.
3. spaces between bars are suggested to range from one-half the width of a bar to the width of a bar.
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4. scales and guidelines are useful aids in reading a chart and should be included.
5. the axes of the chart should be labelled.
6. any “keys” to interpreting the chart may be included within the body of the chart or below the body of the chart.
7. the title of the chart appears either below or above the body.
8. footnotes and source notes, when appropriate, are given following the title of the chart.
Bar Chart (2)
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Bar Chart for Profit of HKTC Co.
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200
400
600
800
1000
1200
1989 1990 1991 1992 1993
Year
Pro
fit
(in
'0
00
)
1989
1990
1991
1992
1993
Bar Chart (3)
Note : Bad debts are excludedSource : ABC Co.
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Grouped Bar Chart
Grouped bar chart is used to depict the magnitudes of two or more grouped data items for different qualitative categories or over time.
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Multiple Bars
Multiple Bars: A number of single bar charts superimposed on top of each other.
The purpose of this chart is to contrast more than one sequence of data values.
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Multiple Bars (2)
(a) Bar Chart for percentage of smokers in age group
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20
40
60
80
100
120
140
Japanese West European East European British
Age Group
Perc
en
tag
e (
%)
Quarter 1
Quarter 2
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(b) Bar chart for quarterly sales of cars
0 20 40 60 80 100 120 140 160
Quarter 1
Quarter 2
Quarter 3
Quarter 4
1993
Sales
British
East European
West European
Japanese
Multiple Bars (3)
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Component Bar Charts
Multiple bars laid directly on top of each other.
Different shading is used to distinguish one set of bars from another.
(c) Component Bar Chart for classification of intaking students
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100
200
300
400
500
600
700
1990 1991 1992 1993 1994
YearN
o. o
f stu
dent
Mature Student
Form 7
Form 5
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Combination Charts
We may use lines and bars to depict the magnitudes of two or more data values for different categories or for different times.
Combination Chart depicting Actual and Estimated Sales over time
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10
20
30
40
50
60
1988
1989
1990
1991
1992
1993
1994
1995
1996
Year
Sale
s (in
'000
) Actual Sales
Estimated Sales
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Pie Charts
Pie Chart for proportion of students
Form 5 Students55%Form 7 Students
30%
Mature Students10%
Others5%
Form 5 Students
Form 7 Students
Mature Students
Others
Pie Chart is used effectively to depict the proportion or percentages of a total quantity by colour or shading
Usually five or fewer categories
Shading for the key or makes more interesting
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Exploded Pies
An exploded pie has one or more segments slightly removed.
An exploded pie gives dramatic effect.
Exploded Pie Chart for proportion of students
55%30%
10%5%
Form 5 Students
Form 7 Students
Mature Students
Others
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Three-dimensional Pies
Using three-dimensions in an exploded pie makes the picture much more eye-catching.
3-D Exploded Pie Chart for proportion of students
Form 5 Students55%
Form 7 Students30%
Mature Students10%
Others5%
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Comparative Pies
compare relative proportions at two different times
Comparative Uses of Different Fuels
1955
45%
15%
40%
1985
40%
45%
15%
Coal
Electricity
Gas
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Pictorial Charts
Pictorial Chart for weekly usage of transportation means
0 1 2 3 4 5 6 7 8 9 10
Car
Bus
Bicycle
MTR
Taxi
Tra
nspo
rtat
ion
Mea
ns
Frequency
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Pictorial Charts (2)
Pictorial symbols are used to depict data to gain attention
Difficult to interpret and also misused at times with the 2-d or 3-d symbols.
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General Features of Data
1. Relative sizes of dataThe following statements concern the relative sizes of data,
Women have a greater life expectancy then men. Men generally taller then women. There is less black and white TV sets than colours.
The most effective way to illustrate measurements of relative size is to use Bar Charts.
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General Features of Data (2)
2. Proportional sizes
The most effective way to illustrate proportional sizes of data is to use Pie Charts.
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3. Change in data over time
Between 1961 and 1981, the relative price index of domestic gas fell steadily whereas that of domestic electricity remained the same.
Consumer spending on personal telephones has steadily risen over the past twenty years.
The most effective way to illustrate changes in data over time is to use Line Charts.
General Features of Data (3)
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4.Pictorial Charts can be designed to both convey the necessary message and to catch eye of the casual reader.
5.The use of words is important for summarising a table or picture, e.g. heading and title, and for conclusion.
General Features of Data (4)
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Using ‘chart junk’ No relative basis
In comparing data Batches
Compressing the Vertical axis No zero point on
the Vertical axis
Errors in Presenting Data
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‘ Chart Junk’
Good Presentation
1960: $1.00
1970: $1.60
1980: $3.10
1990: $3.80
Minimum Wage Minimum Wage
0
2
4
1960 1970 1980 1990
$
Bad Presentation
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No Relative Basis
Good PresentationA’s received by
students.A’s received by
students.
Bad Presentation
0
200
300
FR SO JR SR
Freq.
10%
30%
FR SO JR SR
%
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior
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Compressing Vertical Axis
Good Presentation
Quarterly Sales Quarterly Sales
Bad Presentation
0
25
50
Q1 Q2 Q3 Q4
$
0
100
200
Q1 Q2 Q3 Q4
$
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No Zero Point on Vertical Axis
Good Presentation
Monthly SalesMonthly Sales
Bad Presentation
0
39
42
45
J F M A M J
$
36
39
42
45
J F M A M J
$
Graphing the first six months of sales.
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35
No Zero Point on Vertical Axis
Good Presentation
Monthly Sales Monthly Sales
Bad Presentation
0
20
40
60
J F M A M J
$
36
39
42
45
J F M A M J
$
Graphing the first six months of sales.